Development of a recursive zero annihilator periodic (ZAP) controller with specific applications in flexible space structures

Amy M. Jakubowski; John J. Helferty; David S. Bayard

doi:10.1117/12.174210

1 May 1994 Development of a recursive zero annihilator periodic (ZAP) controller with specific applications in flexible space structures

Amy M. Jakubowski, John J. Helferty, David S. Bayard

Author Affiliations +

Proceedings Volume 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures; (1994) https://doi.org/10.1117/12.174210
Event: 1994 North American Conference on Smart Structures and Materials, 1994, Orlando, FL, United States

Abstract

When continuous-time systems are discretized in the digital controller design process, it is often the case that unstable discrete-time zeros (i.e., zeros outside the unit circle in the Z- plane) result regardless of whether or not there are unstable zeros in the original continuous- time plant. Such a system is recognized as being nonminimum phase. Unfortunately, many design techniques in adaptive control are dependent upon pole-zero cancellations and stable plant invertibility and, therefore, cannot be utilized when the plant is nonminimum phase. In this research, a matrix parameter recursive least squares adaptation law is developed for the zero annihilator periodic (ZAP) controller first introduced by Bayard and later extended by Jakubowski. This direct adaptive control scheme allows for the construction of an optimal set of matrix controller gains that place the transmission zeros of the system at the origin, alleviating the nonminimum phase condition, and force the system output to track a desired reference signal. Simulations are presented that demonstrate the performance of the adaptive ZAP controller on a 12-state, 2-input, 2-output partial model of one of the Astrex struts, where the model of the particular strut exhibits nonminimum phase characteristics.

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Amy M. Jakubowski, John J. Helferty, and David S. Bayard "Development of a recursive zero annihilator periodic (ZAP) controller with specific applications in flexible space structures", Proc. SPIE 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures, (1 May 1994); https://doi.org/10.1117/12.174210

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